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Rado's conjecture Minimal Walks Forcing Axioms S-Space polarized partition relation Prikry-type forcing indecomposable ultrafilter Knaster and friends Precaliber super-Souslin tree Successor of Singular Cardinal Partition Relations Slim tree Selective Ultrafilter Sakurai's Bell inequality coloring number Universal Sequences L-space Distributive tree 54G20 Commutative cancellative semigroups HOD AIM forcing Erdos-Hajnal graphs Weakly compact cardinal stick PFA(S)[S] Local Club Condensation. full tree Dushnik-Miller Constructible Universe Postprocessing function Non-saturation Chromatic number positive partition relation Was Ulam right Rock n' Roll Forcing Dowker space tensor product graph diamond star weak square Lipschitz reduction Vanishing levels Reflecting stationary set Mandelbrot set sap Fat stationary set approachability ideal Successor of Regular Cardinal Martin's Axiom Foundations free Boolean algebra Generalized descriptive set theory Subadditive GMA Singular Density Closed coloring Ulam matrix transformations Cohen real Fast club Club Guessing Ramsey theory over partitions Ineffable cardinal Iterated forcing Almost Souslin Cardinal function Filter reflection regressive Souslin tree Generalized Clubs strongly bounded groups square PFA weak Kurepa tree Ascent Path Shelah's Strong Hypothesis projective Boolean algebra Hindman's Theorem middle diamond Almost countably chromatic Reduced Power Coherent tree Rainbow sets Souslin Tree Diamond Open Access Amenable C-sequence Subtle tree property Hedetniemi's conjecture Aronszajn tree Sierpinski's onto mapping principle Jonsson cardinal Almost-disjoint family Luzin set Hereditarily Lindelöf space Singular cardinals combinatorics very good scale Subtle cardinal Chang's conjecture Large Cardinals club_AD Strongly Luzin set free Souslin tree specializable Souslin tree weak diamond SNR square principles nonmeager set O-space Square-Brackets Partition Relations Analytic sets Prevalent singular cardinals Singular cofinality Nonspecial tree incompactness Antichain Axiom R unbounded function Kurepa Hypothesis Erdos Cardinal Uniformization Diamond-sharp Small forcing ZFC construction countably metacompact Subnormal ideal Sigma-Prikry OCA ccc Poset Uniformly homogeneous higher Baire space Fodor-type reflection C-sequence Strong coloring Diamond for trees Whitehead Problem Well-behaved magma b-scale reflection principles P-Ideal Dichotomy stationary hitting Cardinal Invariants Microscopic Approach Greatly Mahlo Knaster Ostaszewski square Uniformly coherent Absoluteness xbox stationary reflection Parameterized proxy principle
Tag Archives: Singular Density
On topological spaces of singular density and minimal weight
Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading
Workshop on Set Theory and its Applications, February 2007
These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … Continue reading
On the consistency strength of the Milner-Sauer conjecture
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading